Rapid phase transitions defined

Ri does not show any phase transition. This should not be terribly surprising, since, in the deterministic limit, Ri exhibits either class 2 behavior (i.e. periodicity) or class 4 behavior (spatially separated propagating structures with an ill-defined statistical limit). The density p therefore has no well-defined statistical mean for p = 1 and the periodicity and/or propagating structures are rapidly destroyed (and thus p — 0) whenever p < 1. Moreover, from the above mean-field... 

The state of polarization, and hence the electrical properties, responds to changes in temperature in several ways. Within the Bom-Oppenheimer approximation, the motion of electrons and atoms can be decoupled, and the atomic motions in the crystalline solid treated as thermally activated vibrations. These atomic vibrations give rise to the thermal expansion of the lattice itself, which can be measured independendy. The electronic motions are assumed to be rapidly equilibrated in the state defined by the temperature and electric field. At lower temperatures, the quantization of vibrational states can be significant, as manifested in such properties as thermal expansion and heat capacity. In polymer crystals quantum mechanical effects can be important even at room temperature. For example, the magnitude of the negative axial thermal expansion coefficient in polyethylene is a direct result of the quantum mechanical nature of the heat capacity at room temperature." At still higher temperatures, near a phase transition, e.g., the assumption of stricdy vibrational dynamics of atoms is no... 

It follows from Eq. (1.10) that susceptibility increases rapidly at T while order parameter varies smoothly in this vicinity. Such behavior corresponds to known rule [1] that for the second order phase transitions all the properties defined by the first or second derivatives of thermodynamic potential have to vary, respectively, smoothly or abruptly at the transition point. 

The high-dose transition is defined as a transition phase in which the individual suddenly increases the doses of stimulants or switches to smoking (e.g., cocaine crack ) or IV route of administration (Gawin and Ellinwood 1988). This change leads to a rapid escalation of plasma levels and intense euphoria (i.e.. rush) often with subsequent increase in dosing frequency. In its most severe form, the high-dose pattern is characterized by binges of... 

For any of the sol-gel parameters discussed so far, its effect on gel properties can often be followed by an experimental observable known as gel time. Gel time is defined as the time it takes for a solution to undergo a rapid rise in viscosity that corresponds to the transition from a viscous fluid to an elastic gel [9]. At the gel point there is a continuous solid phase containing a structure that reflects the formation and branching of particles under specific growth conditions. This particular phase is important because it is the genesis of structural evolution that takes place in all subsequent processing steps [9, 12]. 

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